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The title says most of it really. How constrained are you in an academic career based on the topic of your PhD thesis? Is it plausible for someome to be researching in an area of math vastly different from their thesis topic later in an academic career, or does it largely determine the scope of research you will be funded for and publish in the future?

I am interested in this as a general question, but I will add some details about my situation that has inspired the question. I am a graduate student at the moment, working in the intersection of homological algebra, triangulated categories, and algebraic geometry. Primarily within sections 18E, 18F, 18G of the AMS subject classification. I'm interested in the future in getting into more pure algebraic geometry research. Is this plausible? It may seem like a stupid question, but my understanding is that there is a much steeper technical learning curve. My current exposure to algebraic geoemtey is roughly a graduate course, so the bulk of chapters 2 and 3 of Hartshorne.

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closed as primarily opinion-based by András Bátkai, Mark Sapir, Sean Lawton, Ben McKay, Chris Godsil Jun 8 '18 at 12:03

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This recent post has many answers to your question: mathoverflow.net/questions/301385/a-second-ph-d-in-mathematics. $\endgroup$ – Valery Isaev Jun 7 '18 at 13:13
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    $\begingroup$ Regarding your specific situation, it doesn't seem like a big leap to make the switch from what you're doing now to more mainstream AG. But these sorts of discussions are always easier in person. $\endgroup$ – Donu Arapura Jun 7 '18 at 14:55

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